Word problem

Question

we have a house on a ten acre plot and we are selling the house with 4 acres. The assessor or treasurer tells us that the house is worth 50,000 and the land 20 thousand. The total tax is 1,000. How much of the tax is attributable to the 6 acres we are selling.

Answer 1

Without making any unfounded assumptions as to the comparative value of the house and the land, the value of the land accounts to 2/7 of the assessment. 

 

(2/7) · $1000 ≈ $285.71

 

The tax on the sold land is

 

(6/10)($285.71) ≈ $171.43

Answer 2

[important note:  Ill approach this as though you meant, "How much of the tax is attributable to the 6 acres we are not selling?" ]

Tax is computed on the assessed value of the property (not the market value).  The problem gives the total value as:  $50,000 + $20,000 = $70,000.  The tax on that total is $1000, or 1/70 the value.

 

Assuming that the land with the house is worth the same amount as the rest of the land, the amount of the land not being sold is 6/10 of $20,000 = $12,000.  At the 1/70 tax rate that means the tax should be:

             (1/70) * $12,000 = $171.43

 

 

This is a proportion in math:

  The total tax is to the total value as the remaining land tax is to the remaining land value

             $1000 / ($50000 + $20000)   =            x                           /  [ (6/10)($20000) ]

               1000/70000 = x /12000

                 1/70 = x / 12000

                 12000 / 70 = x

                   $171.43 = x